The larger fragment sizes of the outer planets will put them in a relatively simple inverse distribution pattern—the largest fragment will be nearest the asteroid belt, and the smallest the furthest out.
If we continue our numbering system, again with a 4-planet spread going from #5 near the asteroid belt, to #8 at the outer limits of the solar system, we can determine some of the basic geophysics.
Most of the heavy elements will not have made it past the asteroid belt layer, so the bulk of material available to the outer planets will be the lighter materials, particularly hydrogen, helium, lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine, and neon. A number of compounds will also occur, namely hydrocarbons, such as methane, from the natural interaction of these elements.
The accumulation on Planets #5-#8 will be in standard spherical distribution; the planets closest to the sun will get the most debris, and hence develop the largest atmosphere. The white dwarf fragments will also be producing these gases in abundance, so the 4 outer planets will be “gas giants,” having a thick gaseous atmosphere, surrounding a hot, white dwarf core will a small amount of heavy matter. The ratio of atmosphere to core will decrease as we move outwards to Planet #8. These planets will look like small suns, because they actually are small suns, without the miles of rock covering up the cores, as found in the inner planets.
Because these are larger fragments, they remain hot for a longer time, and hence “repel” any white dwarf debris. But gravity still pulls, so the larger chunks of debris end up in orbit around these bodies, as moons. The moons then aggregate the bulk of the supernova debris trapped in orbit, and become small “inner-type” planets, rather than having the characteristics of the host planet. The outer planets will have a large number of moons, whereas the inner planets will tend to have few to none.
When the white dwarf debris that makes up the core of a moon drops entirely into the low speed range, it can no longer resist the pull of the host planet, and breaks apart in the gravitational tide, forming a planetary ring, or rings.
In our system, Planets #5 through #8 are Jupiter, Saturn, Uranus, and Neptune.